Details

sample39.0ms

Algorithm

intervals

Results

15.0ms	73×	body	1280	valid
5.0ms	38×	body	640	valid
5.0ms	184×	body	80	valid
3.0ms	30×	body	320	valid
1.0ms	11×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.8b	(- (exp x) 1.0)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

53.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

series68.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

simplify783.0ms

Counts: 58 → 58

prune162.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 1 expressions with local error:

0.2b	(* 1/6 (pow x 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-r`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-l` `prod-exp` `add-cbrt-cube`
2×	`unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

25.0ms

(* 1/6 (pow x 2))

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

(* 1/6 (pow x 2))

simplify1.4s

Counts: 30 → 30

prune73.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
3.9b	(- (/ (exp x) x) (/ 1.0 x))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
4×	`add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`add-exp-log` `associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`cbrt-undiv` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`

Counts

2 → 50

Calls

2 calls:

15.0ms	(/ (exp x) x)
43.0ms	(- (/ (exp x) x) (/ 1.0 x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (exp x) x)
50.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify860.0ms

Counts: 56 → 56

prune175.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (exp x))
0.0b	(/ 1 (/ x (exp x)))
3.9b	(- (/ 1 (/ x (exp x))) (/ 1.0 x))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

103×	`times-frac`
86×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
53×	`add-cube-cbrt`
16×	`associate-/r*`
12×	`add-exp-log`
10×	`add-cbrt-cube` `difference-of-squares`
8×	`div-exp`
7×	`div-inv`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`distribute-lft-out--`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `associate-/r/` `frac-sub` `flip--` `inv-pow`

Counts

3 → 129

Calls

3 calls:

7.0ms	(/ x (exp x))
26.0ms	(/ 1 (/ x (exp x)))
114.0ms	(- (/ 1 (/ x (exp x))) (/ 1.0 x))

series137.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ x (exp x))
45.0ms	(/ 1 (/ x (exp x)))
60.0ms	(- (/ 1 (/ x (exp x))) (/ 1.0 x))

simplify891.0ms

Counts: 138 → 138

prune375.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes43.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.3b

bsearch50.0ms

Steps

Iters	Range		Point
8	-0.0006576197608759923	-2.3499299762321186e-08	-0.00018669778799993176

simplify2.9s

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.0s	2299×	body	1280	valid
262.0ms	1643×	body	640	valid
216.0ms	5388×	body	80	valid
127.0ms	796×	body	320	valid
28.0ms	416×	body	160	valid